Edouard Duchesnay

Robin Louiset, Edouard Duchesnay, Antoine Grigis et al.

Contrastive Analysis VAE (CA-VAEs) is a family of Variational auto-encoders (VAEs) that aims at separating the common factors of variation between a background dataset (BG) (i.e., healthy subjects) and a target dataset (TG) (i.e., patients) from the ones that only exist in the target dataset. To do so, these methods separate the latent space into a set of salient features (i.e., proper to the target dataset) and a set of common features (i.e., exist in both datasets). Currently, all models fail to prevent the sharing of information between latent spaces effectively and to capture all salient factors of variation. To this end, we introduce two crucial regularization losses: a disentangling term between common and salient representations and a classification term between background and target samples in the salient space. We show a better performance than previous CA-VAEs methods on three medical applications and a natural images dataset (CelebA). Code and datasets are available on GitHub https://github.com/neurospin-projects/2023_rlouiset_sepvae.

Robin Louiset, Edouard Duchesnay, Benoit Dufumier et al.

In biomedical Subgroup Discovery, practitioners are interested in discovering interpretable and homogeneous subgroups within a group of patients. In this paper, assuming that healthy subjects (i.e., controls) share common but irrelevant factors of variation with the patients, we motivate and develop a Contrastive Subgroup Discovery method, entitled Deep UCSL. By contrasting patients with controls, Deep UCSL identifies subgroups driven solely by pathological factors, ignoring common variability shared with healthy subjects. Our framework employs a deep feature extractor to learn a discriminative representation space. Mathematically, we derive a novel loss based on the conditional joint likelihood of latent clusters and patient/control labels, optimized via an Expectation-Maximization strategy alternating between subgroup inference and feature encoder updates. A regularization term further encourages representations to capture disease-specific variability while ignoring variability shared with controls. Compared to previous related works, our approach quantitatively improves the quality of the estimated subgroups, as demonstrated on a MNIST example and four distinct real medical imaging datasets. Code and datasets are available at: https://github.com/rlouiset/deep_ucsl.

Carlo Alberto Barbano, Benoit Dufumier, Edouard Duchesnay et al.

Building accurate Deep Learning (DL) models for brain age prediction is a very relevant topic in neuroimaging, as it could help better understand neurodegenerative disorders and find new biomarkers. To estimate accurate and generalizable models, large datasets have been collected, which are often multi-site and multi-scanner. This large heterogeneity negatively affects the generalization performance of DL models since they are prone to overfit site-related noise. Recently, contrastive learning approaches have been shown to be more robust against noise in data or labels. For this reason, we propose a novel contrastive learning regression loss for robust brain age prediction using MRI scans. Our method achieves state-of-the-art performance on the OpenBHB challenge, yielding the best generalization capability and robustness to site-related noise.

Benoit Dufumier, Carlo Alberto Barbano, Robin Louiset et al.

Data augmentation is a crucial component in unsupervised contrastive learning (CL). It determines how positive samples are defined and, ultimately, the quality of the learned representation. In this work, we open the door to new perspectives for CL by integrating prior knowledge, given either by generative models -- viewed as prior representations -- or weak attributes in the positive and negative sampling. To this end, we use kernel theory to propose a novel loss, called decoupled uniformity, that i) allows the integration of prior knowledge and ii) removes the negative-positive coupling in the original InfoNCE loss. We draw a connection between contrastive learning and conditional mean embedding theory to derive tight bounds on the downstream classification loss. In an unsupervised setting, we empirically demonstrate that CL benefits from generative models to improve its representation both on natural and medical images. In a weakly supervised scenario, our framework outperforms other unconditional and conditional CL approaches.

Robin Louiset, Edouard Duchesnay, Antoine Grigis et al.

Contrastive Analysis is a sub-field of Representation Learning that aims at separating common factors of variation between two datasets, a background (i.e., healthy subjects) and a target (i.e., diseased subjects), from the salient factors of variation, only present in the target dataset. Despite their relevance, current models based on Variational Auto-Encoders have shown poor performance in learning semantically-expressive representations. On the other hand, Contrastive Representation Learning has shown tremendous performance leaps in various applications (classification, clustering, etc.). In this work, we propose to leverage the ability of Contrastive Learning to learn semantically expressive representations well adapted for Contrastive Analysis. We reformulate it under the lens of the InfoMax Principle and identify two Mutual Information terms to maximize and one to minimize. We decompose the first two terms into an Alignment and a Uniformity term, as commonly done in Contrastive Learning. Then, we motivate a novel Mutual Information minimization strategy to prevent information leakage between common and salient distributions. We validate our method, called SepCLR, on three visual datasets and three medical datasets, specifically conceived to assess the pattern separation capability in Contrastive Analysis. Code available at https://github.com/neurospin-projects/2024_rlouiset_sep_clr.

Raphael Vock, Edouard Duchesnay, Benoit Dufumier

Contrastive learning (CL) aims to preserve relational structure between samples by learning representations that reflect a similarity graph. Yet, the geometry of the resulting embeddings remains poorly understood. Here we show that weighted InfoNCE objectives can be interpreted as Distance Geometry Problems, where the weighting scheme specifies the target geometry to be realized by the representation. This viewpoint yields exact characterizations of the optimal embeddings for several supervised and weakly supervised objectives. In supervised classification, both SupCon and Soft SupCon (a dense relaxation of it where pairs from distinct classes have small non-zero similarity) collapse samples within each class to a single prototype. However, while balanced SupCon recovers the classical regular simplex geometry, class imbalance breaks this symmetry: SupCon induces non-uniform inter-class similarities depending on class sizes, whereas Soft SupCon preserves a regular simplex geometry regardless of class imbalance. In continuous-label settings, our framework reveals a different failure mode: y-Aware CL generally cannot attain its entropic optimum unless the labels lie on a hypersphere, exposing a mismatch between Euclidean label weights and spherical latent similarity. By contrast, geometrically consistent choices such as Euclidean-Euclidean weighting or X-CLR admit unique optimal embeddings. Our results show that the choice of weighting scheme determines whether contrastive learning is geometrically realizable, degenerate, or inconsistent, providing a principled framework for designing contrastive objectives.

Robin Louiset, Pietro Gori, Benoit Dufumier et al.

Subtype Discovery consists in finding interpretable and consistent sub-parts of a dataset, which are also relevant to a certain supervised task. From a mathematical point of view, this can be defined as a clustering task driven by supervised learning in order to uncover subgroups in line with the supervised prediction. In this paper, we propose a general Expectation-Maximization ensemble framework entitled UCSL (Unsupervised Clustering driven by Supervised Learning). Our method is generic, it can integrate any clustering method and can be driven by both binary classification and regression. We propose to construct a non-linear model by merging multiple linear estimators, one per cluster. Each hyperplane is estimated so that it correctly discriminates - or predict - only one cluster. We use SVC or Logistic Regression for classification and SVR for regression. Furthermore, to perform cluster analysis within a more suitable space, we also propose a dimension-reduction algorithm that projects the data onto an orthonormal space relevant to the supervised task. We analyze the robustness and generalization capability of our algorithm using synthetic and experimental datasets. In particular, we validate its ability to identify suitable consistent sub-types by conducting a psychiatric-diseases cluster analysis with known ground-truth labels. The gain of the proposed method over previous state-of-the-art techniques is about +1.9 points in terms of balanced accuracy. Finally, we make codes and examples available in a scikit-learn-compatible Python package at https://github.com/neurospin-projects/2021_rlouiset_ucsl

Sara Petiton, Antoine Grigis, Raphaël Vock et al.

Linear models are widely used in computational neuroimaging to identify biomarkers associated with brain pathologies. However, interpreting the learned weights remains challenging, as they do not always yield clinically meaningful insights. This difficulty arises in part from the inherent correlation between brain regions, which causes linear weights to reflect shared rather than region-specific contributions. In particular, some groups of regions, including homologous structures in the left and right hemispheres, are known to exhibit strong anatomical correlations. In this work, we leverage this prior neuroanatomical knowledge to introduce a whitening approach applied to groups of regions with known shared variance, designed to disentangle overlapping information across correlated brain measures. We additionally propose a regularized variant that allows controlled tuning of the degree of decorrelation. We evaluate this method using region-of-interest features in two psychiatric classification tasks, distinguishing individuals with bipolar disorder or schizophrenia from healthy controls. Importantly, unlike PCA or ICA which use whitening as a dimensionality reduction step, our approach decorrelates anatomically informed pairs of neuroanatomical regions while retaining the full input signal, making it specifically suited for feature interpretation rather than feature selection. Our findings demonstrate that whitening improves the interpretability of model weights while preserving predictive performance, providing a robust framework for linking linear model outputs to neurobiological mechanisms.

Sara Petiton, Antoine Grigis, Benoit Dufumier et al.

Transfer learning (TL) and deep ensemble learning (DE) have recently been shown to outperform simple machine learning in classifying psychiatric disorders. However, there is still a lack of understanding as to why that is. This paper aims to understand how and why DE and TL reduce the variability of single-subject classification models in bipolar disorder (BD) and schizophrenia (SCZ). To this end, we investigated the training stability of TL and DE models. For the two classification tasks under consideration, we compared the results of multiple trainings with the same backbone but with different initializations. In this way, we take into account the epistemic uncertainty associated with the uncertainty in the estimation of the model parameters. It has been shown that the performance of classifiers can be significantly improved by using TL with DE. Based on these results, we investigate i) how many models are needed to benefit from the performance improvement of DE when classifying BD and SCZ from healthy controls, and ii) how TL induces better generalization, with and without DE. In the first case, we show that DE reaches a plateau when 10 models are included in the ensemble. In the second case, we find that using a pre-trained model constrains TL models with the same pre-training to stay in the same basin of the loss function. This is not the case for DL models with randomly initialized weights.

Carlo Alberto Barbano, Benoit Dufumier, Edouard Duchesnay et al.

Estimating brain age from structural MRI has emerged as a powerful tool for characterizing normative and pathological aging. In this work, we explore contrastive learning as a scalable and robust alternative to supervised approaches for brain age estimation. We introduce a novel contrastive loss function, $\mathcal{L}^{exp}$, and evaluate it across multiple public neuroimaging datasets comprising over 20,000 scans. Our experiments reveal four key findings. First, scaling pre-training on diverse, multi-site data consistently improves generalization performance, cutting external mean absolute error (MAE) nearly in half. Second, $\mathcal{L}^{exp}$ is robust to site-related confounds, maintaining low scanner-predictability as training size increases. Third, contrastive models reliably capture accelerated aging in patients with cognitive impairment and Alzheimer's disease, as shown through brain age gap analysis, ROC curves, and longitudinal trends. Lastly, unlike supervised baselines, $\mathcal{L}^{exp}$ maintains a strong correlation between brain age accuracy and downstream diagnostic performance, supporting its potential as a foundation model for neuroimaging. These results position contrastive learning as a promising direction for building generalizable and clinically meaningful brain representations.

Benoit Dufumier, Pietro Gori, Julie Victor et al.

Contrastive Learning has shown impressive results on natural and medical images, without requiring annotated data. However, a particularity of medical images is the availability of meta-data (such as age or sex) that can be exploited for learning representations. Here, we show that the recently proposed contrastive y-Aware InfoNCE loss, that integrates multi-dimensional meta-data, asymptotically optimizes two properties: conditional alignment and global uniformity. Similarly to [Wang, 2020], conditional alignment means that similar samples should have similar features, but conditionally on the meta-data. Instead, global uniformity means that the (normalized) features should be uniformly distributed on the unit hyper-sphere, independently of the meta-data. Here, we propose to define conditional uniformity, relying on the meta-data, that repel only samples with dissimilar meta-data. We show that direct optimization of both conditional alignment and uniformity improves the representations, in terms of linear evaluation, on both CIFAR-100 and a brain MRI dataset.

Benoit Dufumier, Pietro Gori, Julie Victor et al.

Traditional supervised learning with deep neural networks requires a tremendous amount of labelled data to converge to a good solution. For 3D medical images, it is often impractical to build a large homogeneous annotated dataset for a specific pathology. Self-supervised methods offer a new way to learn a representation of the images in an unsupervised manner with a neural network. In particular, contrastive learning has shown great promises by (almost) matching the performance of fully-supervised CNN on vision tasks. Nonetheless, this method does not take advantage of available meta-data, such as participant's age, viewed as prior knowledge. Here, we propose to leverage continuous proxy metadata, in the contrastive learning framework, by introducing a new loss called y-Aware InfoNCE loss. Specifically, we improve the positive sampling during pre-training by adding more positive examples with similar proxy meta-data with the anchor, assuming they share similar discriminative semantic features.With our method, a 3D CNN model pre-trained on $10^4$ multi-site healthy brain MRI scans can extract relevant features for three classification tasks: schizophrenia, bipolar diagnosis and Alzheimer's detection. When fine-tuned, it also outperforms 3D CNN trained from scratch on these tasks, as well as state-of-the-art self-supervised methods. Our code is made publicly available here.

Benoit Dufumier, Pietro Gori, Ilaria Battaglia et al.

Deep Learning (DL) and specifically CNN models have become a de facto method for a wide range of vision tasks, outperforming traditional machine learning (ML) methods. Consequently, they drew a lot of attention in the neuroimaging field in particular for phenotype prediction or computer-aided diagnosis. However, most of the current studies often deal with small single-site cohorts, along with a specific pre-processing pipeline and custom CNN architectures, which make them difficult to compare to. We propose an extensive benchmark of recent state-of-the-art (SOTA) 3D CNN, evaluating also the benefits of data augmentation and deep ensemble learning, on both Voxel-Based Morphometry (VBM) pre-processing and quasi-raw images. Experiments were conducted on a large multi-site 3D brain anatomical MRI data-set comprising N=10k scans on 3 challenging tasks: age prediction, sex classification, and schizophrenia diagnosis. We found that all models provide significantly better predictions with VBM images than quasi-raw data. This finding evolved as the training set approaches 10k samples where quasi-raw data almost reach the performance of VBM. Moreover, we showed that linear models perform comparably with SOTA CNN on VBM data. We also demonstrated that DenseNet and tiny-DenseNet, a lighter version that we proposed, provide a good compromise in terms of performance in all data regime. Therefore, we suggest to employ them as the architectures by default. Critically, we also showed that current CNN are still very biased towards the acquisition site, even when trained with N=10k multi-site images. In this context, VBM pre-processing provides an efficient way to limit this site effect. Surprisingly, we did not find any clear benefit from data augmentation techniques. Finally, we proved that deep ensemble learning is well suited to re-calibrate big CNN models without sacrificing performance.

Amicie de Pierrefeu, Tommy Löfstedt, Fouad Hadj-Selem et al.

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the interpretability of PCA remains limited. However, in neuroimaging, it is essential to uncover clinically interpretable phenotypic markers that would account for the main variability in the brain images of a population. Recently, some alternatives to the standard PCA approach, such as Sparse PCA, have been proposed, their aim being to limit the density of the components. Nonetheless, sparsity alone does not entirely solve the interpretability problem, since it may yield scattered and unstable components. We hypothesized that the incorporation of prior information regarding the structure of the data may lead to improved relevance and interpretability of brain patterns. We therefore present a simple extension of the popular PCA framework that adds structured sparsity penalties on the loading vectors in order to identify the few stable regions in the brain images accounting for most of the variability. Such structured sparsity can be obtained by combining l1 and total variation (TV) penalties, where the TV regularization encodes higher order information about the structure of the data. This paper presents the structured sparse PCA (denoted SPCA-TV) optimization framework and its resolution. We demonstrate the efficiency and versatility of SPCA-TV on three different data sets. The gains of SPCA-TV over unstructured approaches are significant,since SPCA-TV reveals the variability within a data set in the form of intelligible brain patterns that are easy to interpret, and are more stable across different samples.

Fouad Hadj-Selem, Tommy Lofstedt, Elvis Dohmatob et al.

Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to adhere to domain-specific constraints. Total Variation (TV) enforces spatial smoothness of the solution while segmenting predictive regions from the background. We consider the problem of minimizing the sum of a smooth convex loss, a non-smooth convex penalty (whose proximal operator is known) and a wide range of possible complex, non-smooth convex structured penalties such as TV or overlapping group Lasso. Existing solvers are either limited in the functions they can minimize or in their practical capacity to scale to high-dimensional imaging data. Nesterov's smoothing technique can be used to minimize a large number of non-smooth convex structured penalties but reasonable precision requires a small smoothing parameter, which slows down the convergence speed. To benefit from the versatility of Nesterov's smoothing technique, we propose a first order continuation algorithm, CONESTA, which automatically generates a sequence of decreasing smoothing parameters. The generated sequence maintains the optimal convergence speed towards any globally desired precision. Our main contributions are: To propose an expression of the duality gap to probe the current distance to the global optimum in order to adapt the smoothing parameter and the convergence speed. We provide a convergence rate, which is an improvement over classical proximal gradient smoothing methods. We demonstrate on both simulated and high-dimensional structural neuroimaging data that CONESTA significantly outperforms many state-of-the-art solvers in regard to convergence speed and precision.

Mathieu Dubois, Fouad Hadj-Selem, Tommy Lofstedt et al.

The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited relevance. A penalty like Total Variation (TV) that exploits the natural 3D structure of the images can increase the spatial coherence of the weight map. However, TV penalization leads to non-smooth optimization problems that are hard to minimize. We propose an optimization framework that minimizes any combination of l1, l2, and TV penalties while preserving the exact l1 penalty. This algorithm uses Nesterov's smoothing technique to approximate the TV penalty with a smooth function such that the loss and the penalties are minimized with an exact accelerated proximal gradient algorithm. We propose an original continuation algorithm that uses successively smaller values of the smoothing parameter to reach a prescribed precision while achieving the best possible convergence rate. This algorithm can be used with other losses or penalties. The algorithm is applied on a classification problem on the ADNI dataset. We observe that the TV penalty does not necessarily improve the prediction but provides a major breakthrough in terms of support recovery of the predictive brain regions.